gendist (version 2.0)

qarctan: Quantile function of arc tan model.

Description

Computes qf of the arc tan model.

Usage

qarctan(p, alpha, spec, arg, lower.tail = TRUE, log.p = FALSE)

Arguments

p

scalar or vector of probabilities to compute the qf.

alpha

the value of \(\alpha\) parameter, \(\alpha>0\).

spec

a character string specifying the parent distribution (for example, "lnorm" if the parent distribution corresponds to the lognormal).

arg

list of arguments/parameters of the parent distribution.

lower.tail

logical; if TRUE, probabilities are p, otherwise 1-p.

log.p

logical; if TRUE, probabilities p are returned as log(p).

Value

An object of the same length as p, giving the qf values computed at p.

Details

The qf of arc tan model with parameter \(\alpha\) has a general form of: $$ Q(p) = G^{-1}\left(1-\frac{1}{\alpha} \tan( (1-p)\arctan(\alpha) )\right) $$ for \(a\leq x\leq b\) where \(a\) and \(b\) follow the support of \(G(x)\). \(\arctan\) denote the inverse function of tangent and \(G^{-1}\) is the inverse cdf of parent distribution, respectively. Note also that \(\alpha>0\).

References

Abu Bakar, S. A., Nadarajah, S., Adzhar, Z. A. A. K., & Mohamed, I. (2016). gendist: An R package for generated probability distribution models. PloS one, 11(6). Gomez-Deniz, E., & Calderin-Ojeda, E. Modelling insurance data with the pareto arctan distribution. ASTIN Bulletin, 1-22.

Examples

# NOT RUN {
x=runif(10, min=0, max=1)
y=qarctan(x, alpha=0.5, spec="lnorm", arg=list(meanlog=1,sdlog=2) )
# }